Equilibration of Coordinating Imitation and Best-Response Dynamics

Decision-making individuals are often considered to be either imitators who copy the action of their most successful neighbors or best-responders maximize benefit against current actions neighbors. In context coordination games, where neighboring earn more if they take same action, by means potential functions, it was shown that populations all and equilibrate in finite time when become active update decisions sequentially. However, for mixed two, equilibration only specific activation sequences. It is therefore, unknown, whether a function also exists there actually counter example an sequence prevents equilibration. We show linear graph, number “sections” (a consecutive taking action) serves as function, leading equilibration, this result can extended sparse trees. The existence other types networks remains open problem.